Speed limits in Liouville space for open quantum systems
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One of the defining properties of an open quantum system is the variation of its purity in time. We derive speed limits on the rate of purity change for systems coupled to a Markovian environment. Our speed limits are based on Liouville space where density matrices are represented as vectors. This approach leads to speed limits that are always tighter compared to their parallel speed limits in Hilbert space. These bounds depend solely on the generators of the nonunitary dynamics and are independent of the particular state of the systems. Thus, they are perfectly suited to investigate dephasing, thermalization, and decorrelation processes of arbitrary states. We show that our speed limits can be attained and are therefore tight. As an application of our results we study dephasing of interacting spins, and the speed of classical and quantum correlation erasure in multi-particle system.
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For purity-based quantum speed limits, the Margolus-Levitin type bound is tighter than the Mandelstam-Tamm type bound, but the latter is much easier to compute.
“Similarly to the case of speed limits based on the Bures angle (89) Uzdin and Kosloff [179] again find that the Margolus-Levitin type bound (110) is tighter, but that the Mandelstam-Tamm type bound (106) is much easier to compute.”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [179]
Uzdin and Kosloff derived a Mandelstam-Tamm type bound for the decay rate of purity in open systems, given by equation (105).
“Using the triangle inequality and the Cauchy-Schwarz inequality Uzdin and Kosloff [179] then find |ln (P(τ )) -ln (P(0))| 4 τ 0 dt k A k hs .(105)”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [179]
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Carabba, N. (2024) · Springer theses · doi:10.1007/978-3-031-74179-1_5
Macroscopic theory of multipartite correlations in permutation-invariant open quantum systems
Ptaszyński, K., Chudak, M., & Esposito, M. (2025) · Physical review. E · doi:10.1103/zwfx-m4nq
- Authors
- Uzdin, R., & Kosloff, R.
- Affiliations
- Hebrew University of Jerusalem (IL)
- Corresponding author
- Uzdin, Raam
- Venue
- EPL (Europhysics Letters)
- Publisher
- IOP Publishing
- Published
- 2016-08-01
- Volume
- 115
- Issue
- 4
- Pages
- 40003
- ISSN
- 0295-5075 (ISSN-L)
- 1286-4854
- OpenAlex
- W2460990026
- Cited by
- 52
- References
- 67
- Citations by year
- 2026: 1 · 2025: 4 · 2024: 6 · 2023: 3 · 2022: 12 · 2021: 8 · 2020: 6 · 2019: 5 · 2018: 3 · 2017: 4
- FWCI
- 1.89
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Europhysics Letters (EPL) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Springer Link (Chiba Institute of Technology) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- speed limits, open quantum systems, Liouville space, Markovian environment, dephasing, thermalization, decorrelation, quantum correlations, interacting spins, non-unitary dynamics
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